On the day before the expiration of the contract between the National Football League and the NFL Players Association, negotiators for both sides found themselves deeply divided today over whether the pact permits mandatory testing of players for illegal use of drugs and the fate of unsigned rookies once the agreement runs out.

And they remained light years away from a common ground on which to build a new settlement.

Jack Donlan, the NFL's chief labor negotiator, told the NFLPA that the clubs already have the right to run urinalysis tests on players, and he said he distributed a memorandum about a week ago telling them that. Unsigned rookies, he said, can sign their club's last best offer any time after the expiration of the contract and report to training camp.

Ed Garvey, executive director of the NFLPA, retorted that all unsigned rookies must negotiate through the union after midnight Thursday and can't sign anything on their own.

On the issue of urinalysis, he said, "the players won't do it. If the clubs try it, it would be a unilateral change in working conditions and we would file a complaint with the National Labor Relations Board."

As far as a new agreement is concerned, the union today formally rejected a management offer placed on the table Tuesday that would have raised minimum salaries and bonuses for postseason play and eased the movement of free agents from one team to another.

"It's an insult," said Garvey. "We wait six months and we get an offer like this that doesn't keep pace with the cost of living."

Donlan recessed negotiations abruptly this afternoon after the union rejected his request that it waive its right to be the exclusive bargaining agent for unsigned players with the expiration of the contract.

The union had waived that right as part of the current agreement but, with the expiration of that pact, the right of exclusive representation automatically reverts to the union under federal labor law. Both sides agree that individual negotiations must cease after midnight Thursday and that unsigned players may not report to training camps.

Donlan said he had to leave the meeting to prepare a memorandum for the clubs telling them how to deal with unsigned players. Veteran free agents, he said, can be signed for 110 percent of their 1981 salary and rookies can sign the club's last best offer.

"If they didn't sign it before July 15, why would they want to sign it afterwards?" asked Garvey. He said the NFLPA refused to waive its right of exclusive representation because unsigned players need union protection. As of Friday, 90 rookies and 70 veteran free agents remained unsigned, but many have signed since then, the NFL said.

On the issue of urinalysis, Garvey observed that there have been allegations of illegal use of drugs on Capitol Hill as well as in the NFL in recent weeks.

"Presumably the decisions being made on Capitol Hill are more important than those made on the football field, but nobody's talking about making Congressmen submit to a urinalysis," Garvey said.

Answered Donlan, "we're not trying to punish anyone. We want to help the players who need help. This is serious business. We're talking about men's lives. I have told the clubs they already have the right to give more than one physical examination a year, and they can do a urinalysis for drug use."

The issue of illegal drug use in the NFL has been a major controversy since publication in the June 14 issue of Sports Illustrated of a first-person account of his involvement with cocaine by Don Reese, a former defensive lineman with the Miami Dolphins, the New Orleans Saints and the San Diego Chargers.

Donlan also disputed the characterization of his proposal as an insult. "We feel we've made signifcant advances in many areas. We don't feel it was insulting at all," he said.

But the players, who are seeking a salary scale based on 55 percent of the NFL's gross income, were bitterly disappointed.

Said Mark Murphy, the player representative for the Washington Redskins and a member of the bargaining team, "yesterday was my birthday, but that didn't seem like much of a birthday present. It was like the time when my little sister gave me a doll for my birthday. She thought she was addressing my needs, but she was really addressing her own."

Donlan has said all along that management is adamantly opposed to any proposal that is tied to a percentage of gross income.